fLIBiURYOFCO^TiPtESSj 



tm^' 



f UNITED states' OF AMERICA '- 




THE 



AMERICAN 



Stair-Builders' Guide, 




LUCIUS D. GOULD 



Illustrated by 32 Original Plates. 



NEW YORK: 
A. J. BICKNELL & CO. 

1875. 



y^ 










^ 




Entered according to Act of Congress, in the year 1875, by 

LUCIUS D. GOULD, 
In the Ofifice of the Librarian of Congress, at Washington. 



printed by 

Jennings & Hardham, 

newark, n. j. 



^^ 



^^ 



PREFACE. 



To invent and draw a system of stair-railing superior 
to any heretofore published, is claimed to be impossible. 
But after a careful examination of the systems now in 
use, the author of this work finds that they are not 
faultless, but susceptible of improvements, as will be 
demonstrated and proved to the satisfaction of every one 
who will carefully examine the plates, and peruse the 
descriptive matter shown in this work. 

To furnish such drawings and explanations of the several 
parts of stairs and railing, as can be comprehended by 
workmen not versed in the science, nor much experienced in 
the construction of stair -railing, and as will enable them to 
execute with accuracy the most difficult designs it is neces- 
sary to study simplicity, both in the drawings, and in the 
terms used for their explanation. In what follows, we 
shall aim to do this in such a manner that the inexperienced 
workman will find no difficulty in understanding the plates 
and the description thereof. 

Newaek, N. J.,~ 
August, 1875. 



Plate 1 

Illustrates a few of the principles that govern the operation of constructing the face 
mould for the wreaths, and should be throughly understood by the workman, as 
he will FIEST draw the elliptical curves required for the mould, then find the 
point of contact of the straight wood with the curve and the length required. 

To form an Ellipse with a thread or string. 

Make A B (Figure 1) the long diameter or major axis, and C D half the 
short diameter or minor axis of the required ellipse. From the point D as 
centre, with C B as radius, describe arcs, cutting the major axis at 2 and 3 ; 
at the points, place pins ; around the pins, place a cord so fastened at the 
ends that it shall reach around 2 D 3 ; | place your pencil inside the cord 
and describe the ellipse A D B R. Care should be taken to keep the cord 
to an even tension. Suppose the elliptic curve A D B to be the centre of a 
mould required for a wreath, set off each way from D half the width of the 
rail, and draw the dotted lines D 2 and D 3. From the points S and H 
draw lines parallel to D 2 and D 3 to intersect the major axis. At the 
points thus found, place pins and describe the outside and inside curves. 
To draw two elliptical curves parallel to each other, set off from R to J, 
equal to B N, from the point J as centre, with C N as radius, describe arcs, 
cutting the major axis at A and B, the points for the pins to describe the 
curve required. 

Figure 2 shows the method of finding the point to bore for the first bal- 
uster on the second step, when you have the length of the newel and the 
length of the short baluster given. Let A be the pitch -board and 2 the 
centre of the newel-post ; make 3 4 equal to the difference between the 
lengths of the newel-post and short baluster. Square over from 4 to the 
under-side of newel-cap, and where the line 3 4 intersects the underside 
of rail will be the point to bore for the baluster. To continue the same 
height of rail from the starting to its termination, care should be taken to 
rise from the point B to C, equal to the height of the rise on the second 
flight ; bisect the rise in D for the underside of the level rail. 



Plate 1 




Plate 2 

Exhibits the ground plan and elevation of the hand-rail for a platform 
staircase. 

Figure 2, shows the method of forming the mould for the wreath. Draw 
A B, the pitch or inclination of the stairs. Square up from A and B, equal 
to C D, Fig. 1. Set off from C to B equal to the width of the rail. To 
find the points for the pins, to describe the elliptical curves for the outside 
and inside of the mould ; from the points S and C as centres, with S 2 and 
C 3 as radii, describe arcs, cutting the line A B at 5 4 and 3 2, the points 
required. The application of the spring-bevel, shown at Fig. 3, is seen at 
the joint A, which gives the angle to draw the centre line and determine 
the thickness of plank required for the wreath. The plank sawed square, 
the straight wood one-fourth inch wider than the rail, apply the mould, as 
shown at Fig. 4, mark the curves on both sides. To remove the corner A, 
tack the mould on the opposite side of the plank. The same operation will 
be required to remove the corner B. The saw or plane should be held in 
the direction of the centre line shown at the joint. Screw the wreaths 
together and place them over the pitches on the drawing-board, as shown 
at Fig. 3. Find the points C and D, from which gauge the thickness 
of the rail and form the wreath. 

This system can be applied to large cylinders by extending the radius 
from C to N and leaving the risers the same^distance from the centre of the 
rail, as shown by the dotted lines at Fig. 1. 



Plate 2. 




Plate 3 

Exhibits the ground plan and elevation for a quarter landing ; also the method 
of determining the length of curve required for the mould. 

To draw the elevation, produce the radius A C, Fig. 1, to B, Fig. 2. 
From the point B, draw the pitch and floor lines, indefinitely. From the 
centre of the baluster, shown at A, Fig. 1, draw the dotted line parallel to 
A B, cutting the pitch line at J. Set up from J to P, equal to half the 
height of riser for the centre of level rail. Draw D T parallel to B A. Then 
A T, Fig. 1, is the length of the tangents, and A S is the length of curve 
required. 

In works heretofore published on stair-railing, the authors have given 
geometrical methods, of finding the spring bevels for the joints, which may 
or may not be correct ; the only evidence of their correctness, being ascer- 
tained by their application, which in our method is practically made before 
the mould is djawn, as the width of the mould, and thickness of the plank, 
are determined by the bevels, which can be found by taking a piece any 
thickness and forming the angle ATS, Fig. 1. Draw T L at right angles 
to A T, and L D, the pitch of the stairs. Draw L C at right angles to L 
T. Work to the lines, and apply the bevels. The bevel at C is fer the 
joint. The bevel applied to the pitch line L D, is for the straight wood. 

We will now state to the workman, that the minor or short axis of the 
elliptic curve, required for the mould, must in all cases, be equal to the 
radius of the circle given on the plan. The length of the major or long 
axis, is governed by the angle, to which the cylinder may be cut, as follows : 
Draw A B, Fig. 1, at right angles to A S, equal to S D, Fig. 3 ; produce the 
circle from A to R; draw C D parallel to A B ; join S B and extend to R. 
Then D R equals half the length of the major axis, and S B determines the 
length of curve required for the mould. 

The above rule will in all cases be found true, as we shall prove in the 
following plates. 

The mould for the wreath is shown at Fig. 3. Draw the major axis 
indefinitely. To find the points for the pins, to describe the centre curve, 
set off from C to B, equal to D R, Fig. 1. From the point A, as centre, 
with B, as radius, describe arcs cutting the major axis at 2 and 3, the 
points required. To find the length of curve, from the point B as centre, 
with S B, Fig. 1, as radius, describe an arc, cutting the curve at D, the 
length required. For the direction of the straight wood, draw D S, equal 
to B D, Fig. 2, and B S, equal to A T, Fig. 1 ; then S D is the direction 
required. For the width of the mould, set oflf from A each way half the 
width of the rail ; at Fig. 2, set off from 2 to 3, the width of the rail, draw 
3 4 at right angles to 2 b ; then 4 5 is the width of the mould at B. The 
points for the pins to describe the outside and inside curves, are found in 
the same manner as those for the centre curve ; the plank sawed square to 
a parallel width from the centre curve, one-fourth inch wider than the rail ; 
cut the joints at right angles to the tangents. The application of the bevels 
are shown at Fig. 3, and give the direction of the centre line, from which 
the section of rail is formed at the joints. At right angles to the joints 
draw lines from H and B on both sides of the plank ; then place the centre 
of the mould on the line H D, squared from the joint, and move the mould 
until the line B S stands over the line squared from the joint B. Mark the 
plank for the corners to be removed. The same operation is required for 
the opposite side. Tack the mould on the opposite side of the corner to be 
removed. In doing this, the saw or plane should be held in a vertical 
direction. The surplus wood can be removed from the upper and lower 
sides of the wreath, after tracing the thickness of the rail from the centre 
of the plank. 



Plate 4 

the ground plan for a platform staircase; also a very simple and easy 
method of forming the face mould for the wreath; the planTc sawed square to 
a parallel width. 

The face-mould for the wreath, at Fig. 3, is found by first getting the 
length of the major axis, and describing the elliptical curves; next, the point 
of contact, from that the length of curve required. The length of the major 
axis is obtained by drawing B S, Fig. 1, at right angles to B H, equal to 
H R, Fig. 2. Produce the circle from B to E. Draw J and E D parallel 
to B S ; then J D equals half the length of the major axis, and H S deter- 
mines the length of curve, required for the mould. 

For the mould, at Fig. 3, draw a line indefinitely ; square up from A to 
C, equal to C H, the radius of the circle at Fig. 1 ; set off each way, from 
the point C, half the width of the rail. To find the points for the pins, 
from the point C as centre, with J D as radius, describe arcs, cutting the 
major axis at 2 and 3, the points for the pins, to describe the centre curve. 
The points, for the pins to describe the outside and inside curves, are found 
by drawing the dotted lines parallel to C 2 and C 3, to intersect the major 
axis at the points required. To find the point of contact, draw H J equal 
to 2 3, Fig. 2, from the point J, as centre, with H S, Fig. 1, as radius ; de- 
scribe an arc cutting the curve at S, the point of contact of the straight 
wood with the circle. To find the direction of the straight wood, draw 
J K equal to R P, Fig. 2, and S K equal to T P, Fig. 2. Draw A S, and 
from its intersection with the curves, draw the straight wood parallel to 
K S, indefinitely. The joints are cut at right angles to the tangents. The 
bevel, for the straight wood, is shown at P; for the joint at H, Fig. 2. 

Another example of the practical method of finding the spring bevels 
for the joints : Fig. 4 shows a piece formed to fit the angle B G H, Fig. 1 ; 
draw G S at right angles to G B ; draw S B the same pitch or inclination 
as P T, Fig. 2, and S P the same pitch as P R, Fig. 2 ; apply the bevels at 
right angles to the pitch lines. The bevel on the line S P, is for the joint 
at J; the one on the line S B, is for the joint on the straight wood. 




Scale' /^z indtea = -ifoot. 



Plate 5 

Exhibits the ground, flan of the turn-out at the starting of a staircase, the 
wreath forming its own easing at the newel. 

Before drawing the mould it is necessary to know the height of the newel, 
which is seven inches higher than the short balusters ; or, suppose the short 
baluster to be two feet from the top of the step to the underside of the rail, 
and the newel two feet seven inches from the top of first step to the under- 
side of newel-cap, then at Fig. 3 set up from the top of first step seven 
inches to the centre of rail. To find the position of the steps, from the 
point B, draw the common pitch indefinitely ; set up from the first step the 
height of one riser, cutting the pitch line at C, the point for the riser, which 
determines the position of the steps on the plan. The radius of the curve 
will be governed by the projection of the newel, from the face of string. 
The length of curve will be determined by the width of steps and the 
height of newel. 

Find the major axis of the elliptic curve for the centre of the face-mould 
by drawing S D, Fig, 1, at right angles to S B, equal to L G, Fig. 3 ; pro- 
duce the circle from S to R ; draw R P and C H parallel to S D ; join B D 
and extend to P. Then H P equals half the length of the major axis and 
B D determines the length of curve required for the mould. 

For the face-mould. At Fig. 3 draw the major axis ; square up from the 
point to B, equal to C S, Fig. 1. To find the points for the pins, to 
describe the centre curve, from the point B as centre, with C D as radius, 
describe arcs, cutting the major axis at 3 and 8, the points required. To 
find the length of curve, and point of contact, from the point D as centre, 
with B D, Fig. 1, as radius, describe an arc, cutting the curve at N, the 
point and length required. The direction of the straight wood is given by 
drawing D S equal to B L, Fig. 1, and N S equal to G B, Fig. 3. For 
the width of the mould set off each way from B half the width of the rail. 
At Fig. 3 make 2 3 equal to the width of the rail ; draw 3 4 at right 
angles to 3 3. Then 3 4 is the width of the mould at D. The points for 
the pins to describe the outside and inside curves, are found in the same 
manner as those for the centre curve. 

Figure 4 exhibits a practical method of finding the spring-bevels for the 
joints, by fitting a piece of wood to the angle of the tangents on the plan. 
From the point L, draw the line L C at right angles to L S ; draw D at 
right angles to C L, and C R, the pitch of the stairs ; apply the bevels at 
right angles to the lines, C D and C R. The bevel on the line C D, is for 
the joint 1), and is shown at 3, Fig. 3. The bevel on the pitch-line C R 
is for the straight wood, and is shown at 4, Fig. 3, 



Plate 5 . 




Indies- 1 foot: 



Fig.l 



Plate 6 

Exhibits the plan and elevation for the turnout at the starting of the staircase^ 
the rail terminating against the newel ; the flank sawed square to a parallel 
width. 

The length of the major axis is found by producing the curve D A, Fig. 
1, to T ; draw T J and A S parallel to C B ; make A S equal to R N, Fig. 
2 ; join D S and extend to J. Then P J equals half the length of the major 
axis, and D S determines the length of the curve required for the mould. 

At Fig. 3 draw the major axis indefinitely ; square up from to B 
equal to C D, Fig. 1. The points, for the pins to describe the centre curve, 
are found by taking in the compasses the distance P J, Fig. 1, with the 
point B as centre, and describing arcs, cutting the major axis at 2 and 3, 
the points required. The length of curve, and the direction of the straight 
wood, is found by making C S equal to C B, Fig. 1. From the point S as 
centre, with H N, Fig. 2, as radius, describe arcs, cutting the curve at D 
and H ; join S H and S D. Then H D is the length of curve, and S D the 
direction required. The width of the mould is found by setting off each 
way from B, half the width of the rail ; the points from which to describe 
the outside and inside curves. The points for the pins, are found by draw- 
ing the dotted lines parallel to B 2 and B 3 to intersect the major axis. 
The joints are cut at right angles to the tangents. One bevel answers for 
both joints. 




Scale, tindv- /foot 



Plate 7 

Exhibits the ground plan of an elliptical turnout at the starting of the staircase; 
the 'mould formed ty ordinates; the planTc sawed square, and the joints made 
at right angles to the face of plank. 

The workman will first draw the elliptical curve required fer the turnout, 
and attach the newel cap ; then place the steps as shown at Fig. 1. At 
Fig. 2 is shown the elevation of the steps and risers, which gives the com- 
mon pitch. Set up from the first step to the centre of rail, the diff'erence in 
the heights of the newel post and short baluster, which is 6^ inches; draw 
C L at right angles to A H; make the tangent A B, Fig. 1, equal to C L, 
Fig. 3. From the point B, Fig. 1, draw the tangent B D indefinitely. 

To form the mould for the wreath, draw D S, Fig. 1, at right angles to 
B D, and A S parallel to B D ; set up from D to R equal to L H, Fig. 3 ; 
join R S. At right angles to R S, draw R T, equal to D B, Fig. 1, and S J 
equal to S A, Fig. 1 ; join J T, which should equal C H, Fig. 3; draw any 
number of ordinates from the plan ; transfer the distances, and trace the 
mould. The bevel for the straight wood is shown at Fig. 3, and is found 
by drawing D F at right angles to A B, Fig. 1 ; then by extending F D 
to intersect the pitch line at Fig. 3 ; from the point of intersection, square 
over to K; then P K will equal D F, Fig. 1. From the point P as centre, 
describe an arc, touching the pitch line, which determines the angle for the 
bevel required. 



Plate S 

Exhibits the plan for a staircase, starting with winders; the circle produced 
leyond a quadrant; the plank sawed square to a parallel width, the wreath 
forming its own easing at the newel. 

At Fig. 3, set up from the first step to the centre of rail, the difference in 
the heights of the newel and short baluster, find the height from the first 
step, to the first square step above the winders, which is six risers. Place 
the pitch-board and draw the common pitch indefinitely. Draw the easing, 
so as to have about three inches of straight wood to the wreath. Then from 
the point A, draw the pitch line, tangent to the curve in the rail, which com- 
pletes the elevation. 

The length of the major axis is found at Fig. 1, by producing the curve 
D A to T, and drawing A B and T R parallel to C S; make A B equal to 
C J, Fig. 2 ; join D B and extend to R. Then S R equals half the length 
of the major axis or long diameter, of the elliptic curve required for the 
centre of the mould. 

For the mould, at Fig, 3 draw the major axis indefinitely ; square up 
from C to D, equal to C D, Fig. 1. For the width of the mould, set off 
each way from D half the width of the rail. The points, for the pins to 
describe the centre curve, are found by taking the point D as centre, with 
S R, Fig, 1, as radius, and describing arcs, cutting the major axis at 2 and 
3, the points required. The points, for the pins to describe the outside and 
inside curves, are found by drawing the dotted lines, parallel to D 3 and 
D 2 to intersect the major axis. The length of curve, and direction of the 
straight wood, is found by extending the line C D to S equal to C N, Fig. 
1, from the point S as centre, with R J, Fig. 2, as radius; describe an arc, 
cutting the curve at J, the length required ; join S J and extend to P ; then 
S J is the direction, and J P the length of straight wood required. The 
bevel for the joint at the newel, is shown at R. The bevel, for the straight 
wood, is shown at K. 



Plate 8 [] 




Plate 9 

Exhibits the ground flan and elevation for a staircase^ starting with winders; 
the curve is drawn from centres of unequal radii. 

Set up from the first step to the centre of rail, the difference in the heights 
of the newel and the short baluster. To find the length of the major axis 
of the elliptic curve for the centre of the mould, draw lines from D and A, 
Fig. 1, parallel to C H, indefinitely; set up from D to K, equal to B C, Fig. 
3 ; draw B R, and extend to S. Then J S equals half the length of the 
major axis for the centre of the mould at Fig. 3. 

To form the mould, draw the major axis, indefinitely. To find the points 
for the pins, square up from C to B, equal to C D, Fig. 1. From the point 
B as centre, with J S, Fig. 1, as radius, describe arcs, cutting the major axis 
at 3 and 3, the points required. For the direction of the straight wood 
and length of curve, set up from C to P, equal to C H, Fig. 1. From the 
point P as centre, with L S, Fig. 3, as radius, describe arcs, cutting the 
curve at R and H; join P R and P H; then P H is the direction, and R H 
the length of curve required. For the width of the mould, and the points 
for the pins, to describe the outside and inside curves, set off each way from 
B half the width of the rail; from the points draw lines parallel to B 3 and 
and B 3, to intersect the major axis. The bevel for the joints is shown at 
Fig. 2. 

The face mould for the quadrant at the newel is shown at Fig, 4; square 
up from A to B equal to B 3, Fig. 1 ; set off from A to C equal to S B, Fig. 
3. From the point B as centre, with A C as radius, describe arcs, cutting 
the line A C at 3 and 3 ; the points for the pins to describe the centre curve. 
For the width of the mould, and the points for the pins to describe the 
outside and inside curves, set off each way from B half the width of the rail. 
From the points draw lines parallel to B 3 and B 3 to intersect the line A C. 
The bevel for the joint C is shown at S, Fig. 3. 



Plate 9 



Fi|5. 3. 




^/ ScaZ& / inch - ^ foot 



Plate 10 

Exhib U the ground plan and the e'evation for a staircase^' starting with wind- 

ifx; thu curve drawn J'ri">n centres of unequil radii; the wreath in one piece 

forming its own easings. 

Set up licnu the first step to the point N, equal to ihe diflference in 
the heiglits of the newel, and the short baluster; join R N; square 
over from N to Y ; draw Y V parallel to the centre of rail ; join R V, and 
extend to P. Then H P equals half the major, and V Y half of the minor, 
axis of the quadrant at the starting. 

To find the length of the major axis of the elliptic curve, for the centre 
of the mould, draw lines from the points B and L, Fig, 1, parallel to C P, 
indefinitely ; set up from B to R equal to D G, Pig. 2 ; draw A R and extend 
to D. Then J D equals half the length of the major axis, and A R deter- 
mines the length of curve required. 

To form the mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins,- to describe the centre curve, square up from C to D, 
equal to C B, Fig. 1. From the point D as centre, with J D, Fig. 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
For the point to cut the curve, set up from the major axis equal to 2 3, 
Fig. 1 ; from that point draw a line parallel to the major axis, cutting the 
curve at T. From the point T as centre, with A R, Fig. 1, as radius, describe 
an arc, cutting the curve at N. Then T N is the length of curve required 
for the mould standing over the curve B A, Fig. 1. For the extension of 
the mould over the quadrant at the starting, square over from N to A equal 
to V Y, Fig. 3; draw A B parallel to H N, equal to H P, Fig. 2. To find 
the points for the pins to describe the centre curve from N to B, take A B 
as radius, from the point N as centre, describe arcs, cutting the line A B, for 
the points required. For the width of the mould, set off each way from D 
half the width of the rail. At Fig. 2, 2 3 and 4 5 each equals the width 
of the rail ; then 6 3 equals the width of the mould at T, and R 5 equals 
the width of the mould at B. To find the points for the pins, to describe 
the outside and inside curves from T to D, set off each way from 2 and 3 
equal to T K. The points for the pins, to describe the outside and inside 
curves from N to B, are found in the same manner as those for the centre 
curve. The bevel for the straight wood is shown at 6 ; for the joint B, at R. 



Plate 11 

Exhihits the ground flan for a quarter platform staircase; the risers placed at 
the spring of the cylinder. 

To find the major axis of the elliptic curve for the centre of the mould, 
draw H B, Fig. 1, parallel to C A, equal to S C, Fig. 2; produce the curve 
T H to J; draw T B and extend to J. Then D J equals half the length 
of the major axis, and T B determines the length of curve required. 

At Fig. 3 draw the major axis indefinitely ; square up from C to B equal 
to C T, Fig. 1. To find the points for the pins to describe the centre curve, 
take D J, Fig. 1, as radius, from the point B as centre, describe arcs, cutting 
the major axis at 2 and 3, the points required. To find the point, to 
cut the curve, set up from the major axis, equal to R S, Fig. 1 ; 
from the point, draw a line, parallel to the major axis, cutting the 
curve at 5. From the point 5 as centre, with T B, Fig. 1, as radius, 
describe an arc, cutting the curve at L, the point of contact, and the 
length of curve required. For the direction of the straight wood, draw 5 
H, equal to D, Fig. 2, and L H equal to B D, Fig. 2. Extend H L any 
length required. This being an arbitrary case, it is necessary to find the 
bevels, (which in all cases govern the width of the mould,) which are shown 
at Fig. 2. At Fig. 4 they are enlarged ; the dotted line 3 3 equals the width 
of the rail ; then 2 4 equals the width of the straight wood at L, and 6 5 
the width of the mould at the joint. The points for the outside and in- 
side curves are found by setting oif each way from B, half the width of the 
rail, from the point N, set off each way half the length of 6 5, Fig. 
4 ; then 4 5 and 6 7 are the points from which to draw the curves. The 
points for the pins are found by taking in the compasses C 5 as radius, from 
the point 6 as centre, and describing arcs, cutting the major axis, at the 
points required for the inside curve. The pins for the outside curve are 
found in the same manner. The joints are cut square with the tangents. 



Plate 12 

Exhibits the ground plan and elevation of the flatform^ for an acute angled 
staircase; the, wreath in one piece; the planTc sawed square to a parallel 
width. 

To find the length of the major axis of the elliptic curve for the centre 
of the mould, draw lines from the points A and J, Fig, 1, parallel to C F ; 
set up from A to D, equal to S R, Fig. 2 ; draw R D and extend to E ; then 
E G equals half the length of the major axis, and R D determines the length 
of the curve required for the mould. 

For the mould at Fig. 3, draw the major axis indefinitely. To find the 
points for the pins, to describe the centre curve, square up from C to L 
equal to C R, Fig. 1. From the point L as centre, with G- E, Fig. 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
To find the point to cut the curve, set up from the major axis equal to 2 3, 
Fig. 1 ; from the point, draw a line parallel to the major axis, cutting the 
curve at J. From the point J as centre, with R D, Fig. 1, as radius, describe 
an arc, cutting the curve at R. For the direction of the straight wood, 
draw R H equal to N H, Fig. 2, and J H equal to R H, Fig. 2. For the 
width of the mould, and the points for the pins to describe the outside and 
inside curves, set ofi" each way from L half the width of the rail. From the 
points draw lines parallel to L 2 and L 3 to intersect the major axis. The 
joints are cut square with the tangents, and face of plank. The bevel for 
the joint R is shown at N ; for the straight wood at H. 



Plate 12. 




Scale -/ inchy Ifoot. 



Plate 13 

Exhibits the ground flan and elevation of an acute angled platform staircase; 
the wreath in two 



To find the major axis of the elliptical curve required for the centre of the 
mould. At Fig. 1, draw B S parallel to C R, equal to C D, Pig. 2 ; produce 
the curve A B to D ; join A S and extend to D. Then R D equals half the 
length of the major axis, and A S determines the length of curve required 
for the mould. 

For the face mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins, to describe the centre curve, square up from C to D 
equal to C B, Fig. 1, From the point D, as centre, with R D, Fig. 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
For the point to cut the curve, set up from the major axis equal to L J, 
Fig. 1 ; from the point, draw a line parallel to the major axis, cutting the 
curve at P; from the point P as centre, with A S, Fig. 1, as radius, describe 
an arc, cutting the curve at H ; for the direction of the straight wood, draw 
P R, equal to D B, Fig. 2, and H R equal to S B, Fig. 2 ; for the width of 
the mould, and the points for the pins to describe the outside and inside 
curves, set off each way from D, half the width of the rail ; from the points, 
draw lines parallel to D 2 and D 3, to intersect the major axis. The bevel 
for the centre joint is shown at C ; for the straight wood, at S. 



Plate 13 



Tig 3. 




MR 



c^-. 



Tig.l 



Scale, ^yzirufieS' -ffbot. 



Plate 14 

Exhibits the ground plan and elevation for a quarter platform staircase^ showing 
the position of the riser's in the cylinder, to continue the same plane or inclina- 
tion in the wreath. 

At Fig. 1 set off, from A, to B and D, equal to half the width of the step. 
To find the major axis of the elliptic curve for the centre of the mould, draw 
lines from L and J, Fig. 1, parallel to C A; set up from L to H equal to 
H J, Fig. 2 ; draw S H and extend to R. Then R N equals half the length 
of the major axis. 

For the mould at Fig. 3, draw the major axis indefinitely. To find the 
points for the pins to describe the centre curve, square up from C to B equal 
to C L, Fig. 1; from the point B as centre, with N R, Fig. 1, as radius, 
describe arcs, cutting the major axis at 3 and 3, the points required ; for 
the length of curve, and the direction of the straight wood, set off from C 
to S, equal to C A, Fig. 1 ; from the points C and S as centres, with P J, Fig. 
2, as radius, describe arcs, cutting the curve at H and J ; join S H and S J, 
for the direction required. For the width of the mould, and the points for 
the pins, to describe the outside and inside curves, set off each way from B 
half the width of the rail ; from the points draw lines parallel to B 2 and 
B 3, to intersect the major axis. One bevel answers for the joints. 



Plate 14^. 




\ 



Plate 15 

Exhibits the ground plan and elevation for the landing of the staircase, showing 
the method of finding the length of curve required for the mould, ly which 
the worhnan is not obliged to mahe the joint hi the centre, as the point of in- 
tersection of the level with the p)itch line, determines the length of curve re- 



For the length of the major axis of the elliptic curve for the centre of the 
mould, draw lines from A and S, Fig. 1, parallel to C L ; set up from A to 
B, equal to A B, Fig. 3 ; join H B and extend to R. Then D R equals half 
the length of the major axis, and H B determines the length of the curve. 

For the face mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins to describe the centre curve, set up from C to D equal 
to C H, Fig. 1. From the point D as centre, with D R, Fig. 1, as radius, 
describe arcs, cutting the major axis at 2 and 3, the points required. For 
the direction of the straight wood and length of curve ; from the point 
R as centre, with H B, Fig. 1, as radius, describe an arc, cutting the 
curve at S ; draw R L equal to A L, Fig. 1, and S L equal to H B, Fig. 
3. Then S L is the direction and S R the length of curve required. For 
the width of the mould and the points for the pins to describe the outside 
and inside curves : at Fig. 3, A J equals the width of the rail, and B J equals 
the width of the mould at R ; set oflf each way from D half the width of the 
rail ; from the points describe the curves. The bevel for the straight wood 
is shown at J ; for the joint, at B. 




Centre of RaiO 



SccOe^ 2 'iti,nc/ri- Ifbot. 



r 



Plate 16 

Exhibits the ground plan and elevation for a staircase^ with winders in the 
quarter circle; the wreath in one piece. 

For tlie length of the major axis, of the elliptic curve for the centre of the 
mould : At Fig. 1, from the points A and D, draw lines parallel to C 
L ; set up from A to H equal to R T, Fig. 2 ; join B H and extend to S. 
Then L S equals half the length of the major axis, and B H determines the 
length of curve required for the mould. 

To form the mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins to describe the centre curve, set up from C to B 
equal to C B, Fig. 1. From the point B as centre, with L S, Mg, 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
For the point to cut the curve, set up from the major axis, equal to S T, 
Fig. 2; from the point draw a line parallel to the major axis, cutting the 
curve at S. From the point S as centre, with B H, Fig. 1, as radius, describe 
an arc, cutting the curve at J. For the direction of the straight wood, 
draw J H, equal to N H, Fig. 2, and S H, equal to T H, Fig. 2. For the 
width of the mould, and the points for the pins to describe the outside and 
inside curves, set off each way from B half the width of the rail ; from the 
points draw lines parallel to B 2 and B 3, to intersect the major axis. The 
bevel for the joint J, is shown at S; for the straight wood, at H. 



Plate 17 

Exhibits the ground plan mid elevation of the landing, of an ohtuse a?igled stair- 
case, showing the method of determining the radius of the circle for the 
cylinder. 

From the edge of the drawing-board, square up the line A D. At right 
angles to^A B, draw the floor line and centre of rail. Place the pitch-board 
at D, and draw the pitch, to intersect the centre of rail at H ; draw H B 
parallel to D A ; then A B is the length of the tangents ; draw B S, the 
direction required, to form the obtuse angle ; make B S equal to B A ; draw 
S C at right angles to S B ; then C is the centre, and C A the radius of the 
arc, required for the cylinder. 

To find the length of the major axis, of the elliptic curve for the centre 
of the mould, draw A P, Fig. 1, parallel to C B, equal to C H, Fig. 2 ; join 
S P, and extend to R. Then R H equals half the length of the major axis, 
and S P, determines the length of the curve, required for the mould. 

To form the mould, at Fig. 3, draw the major axis indefinitely. To find 
the points, for the pins to describe the centre curve, square up from C to S, 
equal to C A, Fig. 1 ; set off, from C to P, equal to R H, Fig. 1. From the 
point S, as centre, with C P, as radius, describe arcs, cutting the major axis 
at 3 and 3, the points required. For the length of curve and direction of 
the straight wood, from the point P, as centre, with S P, Fig. 1, as radius, 
describe an arc, cutting the curve at J ; draw P H, equal to S B, Fig. 1, and 
J H, equal to D H, Fig. 3. For the width of the mould, and the points for 
the pins, to describe the outside and inside curves, set off each way from S, 
half the width of the rail ; at Fig. 3, set off from 3 to 3, equal to the width 
of the rail ; then 7 6 equals the width of the mould, at P. The points, for 
the pins, are found in the same manner as those for the centre curve. The 
bevel, for the straight wood, is shown at*B; for the joint, at C. 



Plate 17 



'" n. 




Scale- 1 's indiea^ i foot 



Plate IS 

Exhibits the flan and elevation for a platfoi^m staircase. For want of room, at 
the termination of the return flight, we have placed the riser at the starting, 
leyond the cylinder. 

The length of the major axis, of the elliptic curve, for the centre of the 
mould, is found at Fig, 1, by drawing lines from B and E, parallel to C S, 
indefinitely ; set up, from B to F, equal to R P, Fig. 2 ; join H F, and ex- 
tend to Gr. Then J G equals half the length of the major axis, and H F 
determines the length of the curve, required for the mould. 

For the face mould, at Fig. 3, draw the major axis indefinitely; square 
up from C to P, equal to C B, Fig. 1. To find the points for the pins, to 
describe the centre curve, take J G, Fig. 1, as radius, from the point P, as 
centre, describe arcs, cutting the major axis at 2 and 3, the points required. 
To find the point of contact and length of curve, at any point, set up from 
the major axis, equal to 2 3, Fig. 2 ; from the point, draw a line parallel to 
the major axis, cutting the curve at J. From the point J, as centre, with H 
F, Fig. 1, as radius, describe an arc, cutting the curve at S, For the direc- 
tion of the straight wood, draw J R, equal to P N, Fig. 2, and S R, equal 
to L N, Fig. 2. For the width of the mould, set off each way from P, half 
the width of the rail. The points, for the pins, to describe the outside and 
inside curves, are shown at the intersection of the dotted lines, with the 
major axis. The joints are cut at right angles to the tangents. The bevel 
for the straight wood is shown at N; for the centre joint, at R. 



Plate 19 

ExMlits the ground plan and elevation for the landing of a staircase; the riser 
placed on a line with the face of cylinder; the wreath in two 



The length of the major axis, of the elliptic curve, for the centre of the 
mould, is found by drawing lines from A and P, Fig. 1, parallel to D L ; set 
up, from A to B, equal to A C, Fig. 2 ; draw R B, and extend to C. Then J 
C equals half the length of the major axis, and R B determines the length 
of curve, required for the mould. 

To form the mould, at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins, to describe the centre curve, square up from the 
point C to B, equal to D A, Fig. 1. To find the points, for the 
pins, to describe the centre curve ; from the point B, as centre, with J C, 
Fig. 1, as radius, describe arcs, cutting the major axis at 2 and 3, the points 
required. For the points, to cut the curve, set up from the major axis, equal 
to 2 3, Fig. 2; from the point, draw a line parallel to the major axis, cutting 
the curve at J. From the point J, as centre, with R B, Fig. 1, as radius, 
describe an arc, cutting the curve at L ; then L is the point of contact, and 
L J the length of curve. For the direction of the straight wood, draw J H, 
equal to C D, Fig. 2, and L H, equal to E D, Fig. 2. For the width of the 
mould, and the points for the pins to describe the outside and inside curves, 
set off each way from B, half the width of the rail. From the points, draw 
the dotted lines parallel to B 2 and B 3, intersecting the major axis, at the 
points required. The bevel, for the centre joint, is shown at A; for the 
straight wood, at D, Fig. 2. 

The mould, for the upper wreath, is shown at Fig. 4 ; draw A B, equal to 
A D, Fig. 1. At right angles to A B, draw A C, equal to C F, Fig. 2 ; set 
off, each way from B, half the width of the rail ; join B C. For the width 
of the straight wood ; from the points set off from B, draw the dotted lines 
parallel to B C, to intersect the line A C. The curves are drawn with the 
compasses. The bevel required, is shown at F. 



Plate 20 

Exhihits the continuation of the staircase, shown on Plate 19, to the starting 
of the second flight. 

To find the length of the major axis, of the elliptic curve required for the 
centre of the mould, at Fig. 1, draw lines from the points A and P, parallel 
to S R ; from the point A, set up to B, equal to L B, Fig. 3 ; draw C B, and 
extend to D. Then J D equals half the length of the major axis, and C B 
determines the length of curve required for the mould. 

To form the mould, at Fig. 3, draw a line for the major axis. To find 
the points, for the pins to describe the centre curve, square up from C to S, 
equal to S A, Fig. 1. From the point S, as centre, with J D, Fig, 1, as 
radius, describe arcs, cutting the major axis, at 2 and 3, the points required. 
To find the points, to cut the curve, set up from the major axis, equal to 2 
3, Fig. 2 ; from the point, draw a line parallel to the major axis, cutting the 
curve at D. From the point D, as centre, with C B, Fig. 1, as radius, de- 
scribe an arc, cutting the curve at P. .For the direction of the straight 
wood, draw D H, equal to S C, Fig. 2, and P H, equal to B C, Fig. 3. For 
the width of the mould, and the points for the pins to describe the outside 
and inside curves, set off each way from S, half the width of the rail ; from 
the points, draw lines parallel to S 2 and S 3, cutting the major axis at the 
points required. The bevel, for the straight wood, is shown at S ; for the 
centre joint, at B. 

The mould, for the lower wreath, is shown at Fig. 4. Draw B C, equal to 
S C, Fig. 1, and B A, equal to S H, Fig. 3 ; set off each way from C, half 
the width of the rail. The width of the straight wood, is found by draw- 
ing the dotted lines parallel to A C. The curves are drawn with the com- 
passes. The bevel, for the straight wood, is shown on the line H S. 



I 



Plate 21 

Exhibits the ground 'plan and elevation for a quarter circle of winders, and the 
starting of t?ie return flight, from the spring of the cylinder; the wreath in 
two 



To find the major axis, of the elliptic curve for the centre of the moulds, 
draw lines from A and L, Fig. 1, parallel to C P, indefinitely ; set up from 
A to B, equal to L S, Fig. 2, and from A to D, equal to R H, Fig. 2 ; draw 
S B, and S D, and extend to J and R; produce P C to H, Then H J equals 
half the length of the major axis, of the elliptic curve for the centre of the 
mould, at Fig. 3, and N R equals half the length of the major axis, for the 
mould, at Fig. 4, and S D determines its length. 

For the face mould, at Fig. 3, draw the major axis ; square up from C to 
B, equal to C S, Fig. 1. The points for the pins, to describe the centre 
curve, are found by taking H J, Fig. 1, as radius, from the point B as cen- 
tre, and describing arcs, cutting the major axis at 2 and 3, the points re- 
quired. For the direction of the straight wood, and length of curve, make 
C H equal to C P, Fig. 1. From the points and H, as centres, with 
B S, Fig, 2, as radius, describe arcs, cutting the curve, at S and J ; 
draw H J, and H S, indefinitely. Then J S is the length of curve, and H S 
the direction of the straight wood. For the width of the mould, set 
oflf each way from B, half the width of the rail. The points for the pins, 
to describe the outside and inside curves, are at the intersection of the dot- 
ted lines, with the major axis. The bevel, for the joints, is shown at B.. 

For the face mould, at Fig. 4, draw the major axis ; square up from A to 
B, equal to C A, Fig. 1. The points for the pins, to describe the centre 
curve, are found by taking N R, Fig. 2, as radius, from the point B as centre, 
describe arcs, cutting the major axis at 2 and 3, the points required. To 
find the point of contact, and length of curve, set up from the major axis, 
equal to 3 2, Fig. 2 ; from the point, draw a line parallel to the major axis, 
cutting the curve at H. From the point H, as centre, with S D, Fig. 2, as 
radius, describe an arc, cutting the curve at J. Then H is the point of con- 
tact of the straight wood, with the curve, and H J the length of curve 
required. The direction of the straight wood, is found by drawing J S, 
equal to S G, Fig. 2, and H S, equal to H G, Fig. 2. For the width of the 
mould, set off each way from B, half the width of the rail. The points for 
the pins, to describe the outside and inside curves, are at the intersection 
of the dotted lines, with the major axis. The joints are cut at right angles 
to the tangents. The bevel, for the straight wood, is shown at G ; for the 
centre joint, at S. 



Plate 22 

Exhibits the ground plan and elevation, for a semi-circle of winders, at the 
termination of the staircase ; the wreath in two pieces. 

To find the length of the major axis, of the elliptic curve, required for the 
centre of the mould : At Fig. 1, draw lines from A and E parallel to L C : 
set up from A to B, equal to B S, Fig. 2 ; draw D B, and extend to R. 
Produce L C to H, then H R equals half of the major axis of the ellipical 
curve, for the centre of the mould. 

To draw the face mould, at Fig. 3, draw the major axis indefinitely. To 
find the points for the pins, to describe the centre curve, square up from C 
to D equal to C D, Fig. 1 ; from the point D as centre, with H R, Fig. 1, 
as radius, describe arcs, cutting the major axis at 2 and 3, the points 
required. From the point C as centre, with T R, Fig. 2, as radius ; describe 
arcs, cutting the curve at S and J ; join C S and C J. For the direction of 
the straight wood, draw S B and J B, parallel to C J and C S. To find 
the points for the pins, to describe the outside and inside curves, set off' each 
way from D, half the width of the rail ; from the points, draw the dotted 
lines parallel to D 2 and D 3, intersecting the major axis at the points 
required. One mould answers for both wreaths ; by removing the straight 
wood at J, leaves the mould for the lower wreath ; the same being done 
at S, leaves the mould for the upper wreath. One bevel answers for all the 
joints. 



Plate 22, 




Scaie i inch-= iihot 



Plate 23 

Exhibits the ground plan and elevation of a quarter platform staircase. The 
platform pilaced one step> below the flooi\ to contintie the same width of passage at 
the landing ; the wreath in two pieces. 

For the length of the major axis, of the elliptic curve, for the centre of 
the mould, draw lines from A and J, Fig. 1, parallel to C N ; set up from A 
to L, equal to P L, Fig. 2 ; draw S L, and extend to H. Produce N C to R, 
then R H equals half the length of the major axis, and S L determines the 
length of the curve, required for the face mould, shown at Fig. 3. 

To form the face mould, at Fig. 3, draw the major axis indefinitely ; 
square up from C to S, equal to C A, Fig 1. The points for the pins, to 
describe the centre curve, are found by taking R H, Fig. 1, as radius, with 
the point S as centre, describe arcs, cutting the major axis at 3 and 3, the 
points required. The point of contact, is found by setting up from the 
major axis, equal to 2 3, Fig. 2 ; from the point, draw a line parallel to the 
major axis, cutting the curve at H, the point required. From the point H 
as centre, with S L, Fig. 1, as radius, describe an arc, cutting the curve at 
P. For the direction of the straight wood, draw P R equal to L B, Fig. 2, 
and H R, equal to C B, Fig. 2. For the width of the mould, set off each 
way from S half the width of the rail. The points for the pins, to describe 
the outside and inside curves, are shown at the intersection of the dotted 
lines with the major axis. The bevel shown at C, is^for the straight wood; 
for the joint P, at B. 

The mould for the wreath that connects with the level rail, is shown at Fig. 
4 ; draw the major axis, D B, equal to L D, Fig. 2 ; square up from D to C, 
equal to C A, Fig. 1 ; set off each way from C half the width of the rail ; 
from the points draw the dotted lines parallel to C B, for the width of the 
straight wood at B. The points for the pins, to describe the curves, are 
found by drawing the dotted curves to intersect the major axis. The bevel 
for the straight wood is shown at D, Fig. 2. 



:L_a_ 




Plate 24 

Exhibits the ground plan and elevation, for a staircase, with a quarter circle of 
winders at the landing. 

To find the major axis, of the elliptic curve for the centre of the mould, 
draw lines from the points, J and L, Fig. 1, parallel to B C, indefinitely ; set 
up from J to P, equal to R S, Fig. 3; draw A P, and extend to D ; produce 
B C to H ; then H D equals half the length of the major axis, and A P 
determines the length of the curves, required for the mould. 

For the mould at Fig. 3, draw the major axis indefinitely. To find the 
points for the pins, to describe the centre curve, square up from C to S equal 
to C A, Fig. 1 ; from the point S as centre, with H D, Fig. 1, as radius, 
describe arcs, cutting the major axis, at 2 and 3, the points required. To 
find the points to cut the curve, set up from the major axis, equal to 2 3, Fig. 
2 ; from the point, draw a line parallel to the major axis, cutting the curve 
at P ; from the point P as centre, with A P, Fig. 1, as radius, describe an 
arc, cutting the curve at H. For the direction of the straight wood, draw 
H R, equal to S B, Fig. 2, and P R equal C B, Fig. 2. The points for the 
pins to describe the outside and inside curves are found, by setting oflF each 
way from S half the width of the rail ; from the points, draw lines parallel 
to S 2 and S 3, to intersect the major axis ; the joints are cut at right angles 
to the tangents. The bevel for the centre joint at H, is shown at B, for the 
straight wood, at R. 

The mould for the wreath at the landing, is shown at Fig. 4 ; draw the 
major axis indefinitely, square up from B to H, equal to J, Fig. 1 ; set off from 
B to S, equal to S T, Fig. 2 ; for the width of the mould at S, set off each way 
from H half the width of the rail ; from the points draw lines parallel to H S. 
The points for the pins to describe the curves, are found by describing the 
dotted curves to intersect the major axis. The bevel required for the 
straight wood is shown at T. 



Plate 25 

Exhibits the plan and elevation of a staircase^ starting with a quarter circle of 



To find the major axis of the elliptic curve for the centre of the mould, 
draw lines from H and L, Fig. 1, parallel to R C indefinitely. Set up from 
H to S, equal to P J, Fig, 2 ; draw A S, and extend to D ; produce R C to 
P ; then P D equals half the length of the major axis, and A S determines 
the length of the curve required for the mould. 

To draw the face mould at Fig. 3, draw lines at right angles to each other. 
To find the points for the pins, to describe the centre curve, set up from C, 
to B, equal to C H, Fig. 1. From the point B as centre, with P D, Fig. 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
To find the point to cut the curve, set up from the major axis, equal to 2 3 
Fig. 2 ; from the point draw a line parallel to the major axis, cutting the 
curve at S ; from the point S, as centre, with A S, Fig. 1, as radius, describe 
an arc, cutting the curve at T, For the direction of the straight wood, draw 
T L equal to H S, Fig. 2, and S L equal to J S, Fig. 2. To find the points 
for the pins, to describe the outside and inside curves, set off each way from 
B half the width of the rail ; from the points, draw lines parallel to B 2 and 
B 3, to intersect the major axis. The bevel for joint T, is shown at P, for 
the straight wood at S. 

The mould for the wreath at the starting is shown at Fig. 4 ; draw the 
major axis indefinitely, square up from C to D, equal to A, Fig. 1 ; set off 
from C to L, equal to H V, Fig. 2. For the width of the mould set off each 
way from D, half the width of the rail ; from the points draw lines parallel to 
D L. The points for the pins, to describe the elliptic curves, are shown 
at the intersection of the dotted curves, with the major axis. The bevel is 
shown at H. 



Plate '23. 




Plate 26 

Exhibits the ground plan for a staircase starting with a scroll. At Fig. 1, draw 
the eye one inch wider than the rail ; divide the radius of the eye into four equal 
parts ; set one part off from the centre and form the square; through the 
centre of square draw a line parallel to 4: S ; set off from Gto D the width of 
the rail, and draw the curves that form the scroll. 

To find the major axis of the elliptic curve for the centre of the mould ; 
at Fig. 3, draw lines from H and N, Fig. 1, parallel to J 5, i definitely ; set 
up from H to E, equal to B C, Fig. 2, draw E E and extend to F ; then J F 
equals half the length of the major axis, and R E determines the length of 
curve, required for the mould. 

At Fig. 3, draw the major axis indefinitely. To find the points for the pins 
to describe the centre curve ; square up from C to S equal to R 5, Fig. 1, from 
the point S as centre, with J F, Fig. 1, as radius, described arcs, cutting the 
major axis, at 2 and 3, the points required. To find the point to cut the 
curve, set up from the major axis equal to 2 3, Fig. 2 ; from the point draw 
a line parallel to the major axis, cutting the curve at N ; from the point N 
as centre, with R E, Fig. 1, as radius, describe an arc, cutting the curve at 
H. For the direction of the straight wood, draw N B equal to L S, Fig 2, 
and H B equal to C S, Fig. 2. For the width of the mould, and the points 
for the pins to describe the outside and inside curves, set off each way from 
S, half the width of the rail, from the points, draw lines parallel to S 2, and 
S 3, to intersect the major axis. The bevel for the straight wood, is shown 
on the line 2 S, for the centre joint, on the line S C. 

To draw the mould for the quadrant D R : At fig. 4, draw C B, equal to 4 
R, Fig. 1, and C D equal to P L, Fig. 2. For the width of the mould, set off 
each way from B half the width of the rail, from the points, draw lines parallel 
to B D, to intersect the line C D. The curves are drawn with the com- 
passes. The bevel is shown at L. 



Tig. 3 




Scale inch. - 1 foot. 



Plate 27 

Exh'ibits the ground plan for the turnout, at the starting of the staircase. The 
curve drawn from centres of unequal radie. The wreath in one piece, forming 
its own easings at the newel. 

At Fig. 1, draw the curves, and the newel cap, also the tangents. Produce 
the radius B D, indefinitely, draw L S Fig. 2, at right angles to B D ; set up 
from L to N the height of three raises. Place the pitch board, and draw the 
common pitch. Set up from S to P the diflference in the heights of the 
newel and shoit baluster. To find the positions of the steps, set up from L 
to H, the height of one riser, draw H J parallel to L S, cutting the pitch at 
the point required for the face of the riser, which determines the position of 
the steps on the plan. 

For the length of the major axis of the elliptic curve for the centre of the 
mould, draw D P, Fig. 1, parallel to B C, equal to E N, Fig. 2 ; draw L P 
and extend to J ; then H J equals half the length of the major axis, and L 
P determines the length of curve, required for the mould. 

For the mould at Fig. 3, draw the major axis indefinitely. To find the 
points for the pins to describe the centre curve, square up from C to D 
equal to B D, Fig. 1. From the point D as centre, with H J, Fig. 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
For the width of the mould and the points for the pins to describe the 
outside and inside curves, set off each way from D half the width of the 
rail. From the points, draw lines parallel to D 2 and D 3, to intersect the 
major axis. For the length of curve, and direction of the straight wood 
set up from C to L equal to B C, Fig 1 ; from the point L as centre, with R 
N, Fig 3, as radius, describe arcs, cutting the curve at S and P, draw L S 
and L P indefinitely ; set off from L to R equal to R P, Fig. 2, draw R H at 
right angles to L R equal to R S, Fig. 1 ; extend the tangent S L to T equal 
to L P, join T H, set off from S to A, equal to D G, Fig. 1, draw A H, indefi- 
nitely. From the point N as centre, describe the curve from H, tangent to 
the curve S D ; through the point N, draw the dotted line at right angles 
to the tangent L R, on which find the centres to describe the outside and 
inside curves. The width of the mould is shown at Fig. 2 ; by setting off 
from 2 to 3, equal to the width of the rail, then the bevel determines the 
width of the mould at H. The bevel for the straight wood is shown at E, 
Fig. 2, for the joint at R, 

At Fig. 4 is shown a practical method of finding the spring bevels for the 
joints; form a piece to fit the angle D N R, Fig. 1, draw B A at right 
angles to N B, and B C the pitch of the rail. Work to the lines and apply 
the bevels as shown, the bevel applied to the line B C is for the straight 
wood. The one shown as S is for the joint at the newel. 



Plate 28 

Exhibits the ground plan and elevation for a platform staircase, the risers 
beyond the cylinder. 



To find the length of the major axis of the elliptic curve for the centre 
of the mould, draw lines from D and H, Fig. 1, parallel to C J indefinitely. 
Set up from D to. S, equal to B S, Fig. 2, draw P S, and extend to R ; then 
J R equals half of the length of the major axis, and P S determines the 
length of the curve required for the mould. 

To draw the mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins, to describe the centrecurve, square up from C to B, 
equal to C P, Fig. 1. From the point B as centre, with J R, Fig 1, as 
radius, describe arcs, cutting the major axis at 2 and 3, the points required. 
To find the points, to cut the curve, set up from the major axis, equal to L 
J, Fig. 2 ; from the point, draw a line parallel to the major axis, cutting the 
curve at J. From the point J as centre, with P S Fig. 1, as radius, describe 
an arc, cutting the curve at P. For the direction of the straight wood, 
draw J H, equal to S L, Fig. 2, and P H equal to N L, Fig. 2. For the 
width of the mould, and the points for the pins, to describe the outside and 
inside curves, set off each way from B, half the width of the rail ; from the 
points draw lines parallel to B 2 and B 3, to intersect the major axis. The 
bevel for the centre joint is shown at A, for the straight wood at L. 



Plate 29 

Exhibits the ground plan and elevation, for a staircase with a semi-circle of 
winders ; the wreath formed in three pieces. 

To find the length of the major axis of the elliptic curve, for the centre of 
the mould, draw D S, Fig. 1, equal to L E, Fig. 3; join J S and extend to 
R; then P R equals half the length of the major axis required. 

To draw the mould at Fig. 3, draw the major axis indefinitely. To find 
the points for the pins, to describe the centre curve, square up from C to D, 
equal to C D, Fig. 1 ; from the point D as centre, with P R, Fig. 1, as radius, 
describe arcs, cutting the major axis at 2 and 3, the points required. For 
the direction of the tangents, and length of curve, make C B equal to C 
N, Fig. 1 ; from the point B as centre, with E G, Fig. 2, as radius, describe 
arcs, cutting the curve, at S and R; join B S and B R, the direction and 
length required. For the width of the mould, and the points for the pins, 
to describe the outside and inside curves, set off each way from D half the 
width of the rail ; from the points draw lines parallel to D 3 and D 3, to 
intersect the major axis. The joints are cut at right angles to the tangents. 
One bevel answers for all the joints. 




6S avBta: 



Plate 30 

ExTiihits the ground flan and elevations, for two staircases starting with winders ; 
the wreath in one piece. 

At Fig. 2, we have placed the centre of rail, at the newel, the height of 
one riser above the step, to increase the length of the easing, which added 
to the length of short baluster, gives the length of the newel, from the step 
to the cap. The pitches over the winders, are drawn, to give an easy and 
graceful curve to the rail when finished. 

To find the major axis of the elliptic curve for the centre of the mould, 
draw N P and D S, Fig. 1, parallel to C R, indefinitely ; set up from D to S» 
equal G J, Fig. 2, join H S and extend to P ; then R P, equals half the 
length of the major axis, and H S, determines the length of the curve 
required for the mould. 

At Fig. 3, draw the major axis indefinitely. To find the points for the pins, 
to describe the centre curve, square up from C to D, equal to H, Fig. 1. 
From the point D as centre, with R P, Fig. 1, as radius, describe arcs, 
cutting the major axis at 3 and 4, the points required. For the point to cut 
the curve, set up from the major axis, equal to N 4, Fig. 2, from the point, 
draw a line parallel to the major axis, cutting the curve at S ; from the point 
S, as centre, with H S, Fig. 1, as radius, describe an arc, cutting the curve 
at B. For the direction of the straight wood, draw B H, equal to S 4, Fig. 
2, and S H, equal to J 4, Fig. 2. For the width ot'the mould, and the points 
for the pins to describe the outside and inside curves, set off each way from 
D half the width of the rail ; from the points, draw lines parallel to D 3 and 
D 4, to intersect the major axis. The bevel for the joint at S, is shown at B, 
for the joint L, is shown at T, Fig. 2. 

Fig. 4 is the same as Fig. 1, with two additional steps at the starting. 
Set up from the first step to the centre of rail, the difference in the heights 
of the newel and short baluster. Make B A, equal to A B, Fig. 4, describe 
the curve for the easing ; from the point H, draw the pitch line tangent to 
the curve. The mould at Fig. 6, is drawn in the same manner as that shown 
at Fig. 3. 



Plate 31 

ExMhits the ground planfoi' a circular staircase ; the wreath in four pieces. 

To find the common pitch, at Fig. 2, extend the tangent C D to A ; at right 
angles to A C, draw A J, equal to five risers, join C J ; then C J is the pitch 
of the tangents, that meet at the joints F C and N. 

At Fig. 1, extend the tangent, S B, to V, equal to B F ; from the points V 
B S, and A, draw lines parallel to O S, and at right angles V A, indefinitely. 
At any point H, Fig. 3, square over for the first step ; set up from E to C 
the height of two risers, from H to R the height of five risers, and from E to F, 
the difference in the height of the newel and short baluster ; join R and 
extend to S, then R and S are the points from which the pitches are drawn. 
Draw R P the common pitch, or the same inclination as J C Fig. 2 ; 
join P S and extend to J; then R P, P L and L J are the tangents required 
for the mould. 

To find the length of the major axis of the elliptic curve required for the 
of the mould : At Fig. 1, draw lines from F and N, parallel to O B, indefi- 
nitely; set up from F to K, equal to N R, Fig. 3; join S K, and extend to 
L ; then W L equals half the length of the major axis required. 

The mould for the wreath, at the starting, is shown at Fig. 5. Draw the 
major axis indefinitely. To find the points for the pins, to describe the 
centre curve, square up from C to D, equal to O S, Fig. I, from the point D 
as centre, with W L, Fig. 1, as radius, describe arcs, cutting the major axis, 
at 2 and 3, the points required ; set up from C to S, equal to O B, Fig. 1. 
From the point S as centre, with P R, Fig. 8, as radius, describe arcs, cutting 
the curve at R and L ; draw S R, and S L indefinitely. For the width of 
the mould, and the points for the pins, to describe the outside and inside 
curves, set off each way from D half the width of the rail; from the 
points, draw lines parallel to D 2 and D 3, to intersect the major axis. To 
draw the extension of the mould, standing over the curve S 2, on the plan, 
set off from S to T, equal to P L, Fig. 3, and from T to H, equal to L J Fig. 
3 ; draw T P and H J at right angles S H, make T P, equal to R S, and H 
J equal to 2 3, Fig. 1. At Fig. 3, 4 5 equals the width of the rail, then L 5 
is the width of the mould at J ; find the centres on the line, T P as shown by 
the dotted lines, and with the compasses, describe the curves, tangental to 
the elliptical curves, all ready drawn. The bevels for the joints are shown 
at Fig. 3. 

To find the length of curve on the plan, for the wreath at the landing : At 
Fig. 4, from the point N, draw the common pitch indefinitely ; set up from 
the line N B, to the fioor, the height of two risers, and from the floor to the 
centre of the level rail, half the height of one riser from the point to bore 
for the first baluster on the floor ; from the point, draw a line parallel to N 



B, cutting the pitch at D ; from the point D, draw D B at right angles to N 
B ; from the point B as centre, with B N as radius, describe an arc, cutting the 
curve at R ; join B R, then N R is the length of curve required. 

To find the length of the major axis of the elliptical curve, required for 
the centre of the mould, shown at Fig. 6 : Draw lines fromN and G, Fig. 1, 
parallel to O D indefinitely. Set up from N to L, equal to A J, Fig. 2, draw 
C L and extend to X ; then H X equals half the length of the major axis. 

At Fig. 6, draw the major axis indefinitely. To find the points for the 
pins, to describe the centre curve, from the point B as centre, with H X, Fig. 1, 
as radius, dfescribe arcs, cutting the major axis at 3 and 3, the points required. 
For the width of the mould, and the points for the pins, to describe the outside 
and inside curves, set off each way from B half the width of the rail ; from the 
points draw lines parallel to B 2 and B 3, to intersect the major axis. For the 
length of curve required for the wreath, standing over C N on the plan, set 
up from C to T, equal to O D, Fig. 1. From the point T, as centre, with C 
V, Fig. 2, as radius, describe arcs, cutting the curve at H and J ; join T H 
and T J, the lines from which to square the joints. The bevel is shown at 
Fig. 2. 

For the length of the mould at the landing, square up from N to S, equal 
to B R, Fig. 4. From the point S, as centre, with N D, Fig. 4, as radius, 
describe an arc, cutting the curve at R. For the direction of the tangent, 
set up from N to P, equal to S R, Fig. 4, draw P R, the direction required. 
The bevels for the joints are shown at Fig. 4. 



Plate 32 

Exhibits the ground plan of an elliiMcal staircase^ the planTc for the wreaths 
sawed square to a parallel width, the joints cut at right angles to the face of 
the plank. 

To find the common pitch, at Fig. 1, extend the tangent A B to C, draw 
A D at right angles to A C, equal to seven risers ; join C D, then C D is the 
pitch of the tangents that meet at the joints L and A. 

The mould for the centre wreath is shown at Fig. 3. Draw the dotted 
chord A L, square up from A and L indefinitely. Through the point B, 
draw E F, parallel to the dotted chord ; make E H equal to A D, Fig. 2 ; 
join F H, produce OB to N ; draw F R and H J at right angles to F H, 
equal to E A and F L ; join N R and N J, which should equal P C and P 
D, Fig. 3 ; draw any number of ordinates and transfer the distances, through 
the points trace the mould. The bevel for the joint is shown at Fig. 2. 

At Fig. 4, is shown the development of the tangents, at the starting. 
From the point A, draw the first step ; set up to H the centre of rail four 
inches, which, added to the short baluster, gives the height of the newel ; 
set up from A to B five risers, draw B C the common pitch, join C H. At 
Fig. 1, extend the tangent L D to H, then L H equals S D, Fig. 4 ; from the 
point J, draw J H, the directing ordinate, indefinitely ; from the points L 
and D, draw lines parallel to J H ; through the point D, draw the seat at 
right angles to J H ; set up from R to G, equal to S B, Fig. 4 ; square up 
from K to F, equal to J 3, Fig. 1, and from G to P, equal to L 2, Fig. 1 ; 
join S F and S P, then S P will equal C B, and S F will equal C L, Fig. 4 ; 
draw any number of ordinates from the plan, transfer the distances, and 
through the points trace the mould. The bevel for the joint F, is shown at 
C ; for the joint P, at S, Fig. 4. 

The mould for the quadrant at the scroll, is found by drawing 5 7, equal 
to H L, Fig. 4, and 7 8 equal to 5 J. To find the points for the pins, to 
describe the centre curve, from the point 8 as centre, with 8 9 as radius, 
describe arcs, cutting the line 5 7, the points required. For the width of 
the mould and the points for the pins, to describe the outside and inside 
curves, set off each way from 8 half the width of the rail ; from the points 
draw lines parallel to 8 4 to intersect the line 5 7. The bevel fer the joint 
at 5 is shown at L, Fig. 4. 

The length of curve on the plan, required for the mould, at the landing, 
is found at Fig. 6. From the point A, draw the pitch line parallel to C D, 
Fig. 2, indefinitely ; set up from the line A L, the height of four risers, to the 
floor ; set up from the floor to centre of level rail, half a rise from the point 
to bore for the flrst baluster ; from the point, draw a line to intersect the 
pitch line at C ; from the point C, drop a line at right angles to A L, 



Plate 32. 





Sialf. inch. - /foot 



cutting the line from A at L ; draw L P tangent to tlie curve on the plan, then 
A P is the length of curve required, and P L is the directing ordinate for 
the mould. 

To draw the mould at Fig, 7 : From the point L, draw the seat at right 
angles to L P ; set up from S to R, equal to L C, Fig. 6 ; join L R ; square 
up from L to H, equal to L P ; from R to B, equal to S A ; join L B, 
which should equal A C, Fig. 6. Draw the ®rdinates, transfer the distances, 
and through the points trace the mould. The bevel for the joint H, is 
shown at R ; for the joint B, at Fig. 6. 



LIST OF PEACTICAL BOOKS 

PUBLISHED AND FOB SALE BY 

j^. jr. bicieci^eiXjXj & co. 

27 WABREN STBEET, NEW TOBK. 



Atwood's Architectural Proportions. . $1 00 

Atwood's Country and Suburban Residences .... 1 50 

Baumann's Foundations 75 

Bicknell's Village Builder and Supplement 12 00 

Bicknell's Supplement to Village Builder 5 . 00 

Bicknell's Detail Cottage and Constructive Arch 10 00 

Bell's Carpentry Made Easy 5 00 

Boyce's Art of Lettering 3 50 

Boyce's Modern Ornamenter 3 50 

Burns' Architectural Drawing-Book 1 00 

Burns' Illustrated and Perspective Drawing-Book 1 00 

Burns' Ornamental Drawing-Book 1 00 

Butler's Ventilation of Buildings . . 50 

Cummings & Miller's Architectural Details 10 00 

Cummings' Architectural Details 10 00 

Croflf 's Front Entrance Doors 5 00 

Croff 's Progressive American Architecture 10 00 

Copley's Plain and Ornamental Alphabets 3 00 

Dearborn's Text Book of Letters 3 00 

Dearborn's Scrolls 3 50 

Eveleth's School-House Architecture 6 00 

Esser's Draughtsman's Alphabets 150 

Free Hand Drawing 50 

Gould's Carpenter's and Builder's Assistant 3 00 

Guillaume's Interior Architecture 3 00 

Harney's Barns and Out Buildings 6 00 

House of God '■'• ; 1 75 

How to Paint 1 00 

Hussey's National Cottage Architecture 6 00 

Hallett's Builders' Specifications 1 75 

Hallett's Builders' Contracts 10 

Hinkle & Co's Book on Building ; paper, |1 00 ; cloth 1 50 

Lewis' Practical Poultry Keeper ..... 1 50 

Lakey's Village and Country Houses 6 00 

Mechanic's Own Book 1 50 

Mechanic's Text Book 75 

Mitchell's Stepping Stone to Architecture 60 

Ornamental Designs for Fret Sawing 60 

Sawyer's Fret Sawing 1 50 

Silloway's Carpentry • 3 00 

Tower's Bridge Building 3 00 

Vose's Manual for Railroad Engineers 13 50 

Vogde's Price-Book ; cloth, $1 50 ; morocco 3 00 

Woodward's National Architecture 13 00 

Woodward's Country Homes 150 

Withers' Church Architecture 15 00 

Williams' Window Gardening 1 50 

Wooden and Brick Buildings, with details, 3 vols., $9 00 each 18 00 

All the above books mailed and post paid on receipt of price. Illustrated 
Catalogue mailed free to any address. 



